• On the quaternionic curves according to parallel transport frame 

  Soyfidan, Tülay; Parlatıcı, Hatice; Güngör, Mehmet Ali (2013)

  In this paper, we have studied parallel transport frame for a quaternionic curve in E3 and E4. Firstly, we have defined a new kind of slant helix with respect to parallel transport frame and given some necessary and ...
• Some sequence spaces derived by Riesz mean in a real 2-normed space 

  Başarır, Metin (SPRINGER INTERNATIONAL PUBLISHING AG, 2014)

  In the present paper, we introduce some new sequence spaces derived by Riesz mean and the notions of almost and strongly almost convergence in a real 2-normed space. Some topological properties of these spaces are investigated. ...
• Fibonacci Generalized Quaternions 

  Akyiğit, Mahmut; Kösal, Hidayet Hüda; Tosun, Murat (SPRINGER BASEL AG, 2014)

  In this paper, the Fibonacci generalized quaternions are introduced. We use the well-known identities related to the Fibonacci and Lucas numbers to obtain the relations regarding these quaternions. Furthermore, the Fibonacci ...
• Commutative Quaternion Matrices 

  Kösal, Hidayet Hüda; Tosun, Murat (SPRINGER BASEL AG, 2014)

  In this study, we introduce the concept of commutative quaternions and commutative quaternion matrices. Firstly, we give some properties of commutative quaternions and their fundamental matrices. After that we investigate ...
• ON THE SPECTRA OF SOME MATRICES DERIVED FROM TWO QUADRATIC MATRICES 

  Özdemir, Halim; Petik, Tuğba (SPRINGER SINGAPORE PTE LTD, 2013)

  The relations between the spectrum of the matrix Q + R and the spectra of matrices (gamma + delta)Q + (alpha+ beta)R - QR - RQ,QR - RQ, alpha beta R - QRQ, alpha RQR - (QR)(2), and beta R - QR have been given assuming that ...
• Forced Vibration of the Pre-Stressed and Imperfectly Bonded Bi-Layered Plate Strip Resting on a Rigid Foundation 

  Hazar, Elman; Eröz, Mustafa (TECH SCIENCE PRESS, 2013)

  Within the scope of the piecewise homogeneous body model with utilizing of the three dimensional linearized theory of elastic waves in initially stressed bodies the influence of the shear-spring type imperfection of the ...
• GENERALIZED FIBONACCI AND LUCAS NUMBERS OF THE FORM wx(2) AND wx(2) 1 

  Keskin, Refik (KOREAN MATHEMATICAL SOC, 2014)

  Let P >= 3 be an integer and let (U-n) and (V-n) denote generalized Fibonacci and Lucas sequences defined by U-0 = 0,U-1 = 1; V-0 = 2,V-1 = P, and Un+1 = PUn Un-1 Vn+1 = PVn - Vn-1 for n >= 1. In this study, when P is odd, ...
• ON THE mth DIFFERENCE SEQUENCE SPACE OF GENERALIZED WEIGHTED MEAN AND COMPACT OPERATORS 

  Başarır, Metin (SPRINGER, 2013)

  In this article, using generalized weighted mean and difference matrix of order m, we introduce the paranormed sequence space l(u, v, p; Delta((m))), which consist of the sequences whose generalized weighted Delta((m))-difference ...
• On the strong and Delta-convergence of new multi-step and S-iteration processes in a CAT(0) space 

  Başarır, Metin; Şahin, Aynur (SPRINGER INTERNATIONAL PUBLISHING AG, 2013)

  In this paper, we introduce a new class of mappings and prove the demiclosedness principle for mappings of this type in a CAT(0) space. Also, we obtain the strong and Delta-convergence theorems of new multi-step and ...
• ON SOME COMBINATORIAL IDENTITIES INVOLVING THE TERMS OF GENERALIZED FIBONACCI AND LUCAS SEQUENCES 

  Halıcı, Serpil (HACETTEPE UNIV, FAC SCI, 2013)

  In this paper, we consider the Horadam sequence and some summation formulas involving the terms of the Horadam sequence. We derive combinatorial identities by using the trace, the determinant, and the nth power of a special ...
• Proof of a conjecture related to the parabolic class numbers of some Fuchsian groups 

  Keskin, Refik (ELSEVIER SCIENCE INC, 2005)

  This paper proves a conjecture given in [6], which is concerning with the parabolic class numbers of some Fuchsian groups.
• On generalized difference lacunary statistical convergence in a paranormed space 

  Altundağ, Selma (SPRINGEROPEN, 2013)

  In this article, we introduce the concept of -lacunary statistical convergence and -lacunary strong convergence in a paranormed space. Also, we establish some connections between these concepts.
• A note on the roots of some special type polynomials 

  Halıcı, Serpil (SPRINGER INTERNATIONAL PUBLISHING AG, 2013)

  We give some fundamental properties related to them. Also, we obtain asymptotic results for the roots of polynomials G(n)((k))(X).
• On the Diophantine equation x(2) - kxy plus y(2)-2(n)=0 

  Keskin, Refik; Karaatlı, Olcay (SPRINGER HEIDELBERG, 2013)

  In this study, we determine when the Diophantine equation x (2)-kxy+y (2)-2 (n) = 0 has an infinite number of positive integer solutions x and y for 0 a (c) 1/2 n a (c) 1/2 10. Moreover, we give all positive integer solutions ...
• Positive integer solutions of the diophantine equation x(2)-L(n)xy +(-1)(n)y(2) = +/- 5(r) 

  Keskin, Refik (SPRINGER INDIA, 2014)

  In this paper, we consider the equation x (2)-L (n) x y+(-1) (n) y (2) = +/- 5 (r) and determine the values of n for which the equation has positive integer solutions x and y. Moreover, we give all positive integer solutions ...
• POSITIVE INTEGER SOLUTIONS OF THE DIOPHANTINE EQUATIONS x(2)-5F(n)(xy)-5(-1)(n)y(2) = +/- 5(r) 

  Keskin, Refik; Karaatlı, Olcay (UNIV MISKOLC INST MATH, 2013)

  In this study, we consider the Diophantine equations given in the title and determine when these equations have positive integer solutions. Moreover, we find all positive integer solutions of them in terms of Fibonacci and ...
• A note on some Fuchsian groups 

  Keskin, Refik (SPRINGER, 2005)

  In this paper, we introduce some Fuchsian groups and calculate their parabolic class numbers. In addition, we give two conjectures concerning with the parabolic class number.
• On the strong and Delta-convergence of SP-iteration on CAT(0) space 

  Şahin, Aynur; Başarır, Metin (SPRINGER INTERNATIONAL PUBLISHING AG, 2013)

  MSC: 47H09, 47H10.
• Decay and growth estimates for solutions of second-order and third-order differential-operator equations 

  Yılmaz, Yalçın (PERGAMON-ELSEVIER SCIENCE LTD, 2013)

  We obtained decay and growth estimates for solutions of second-order and third-order differential-operator equations in a Hilbert space. Applications to initial-boundary value problems for linear and nonlinear non-stationary ...
• Split Fibonacci Quaternions 

  Akyiğit, Mahmut; Tosun, Murat; Kösal, Hidayet Hüda (SPRINGER BASEL AG, 2013)

  Starting from ideas given by Horadam in [5] , in this paper, we will define the split Fibonacci quaternion, the split Lucas quaternion and the split generalized Fibonacci quaternion. We used the well-known identities related ...

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